You could use a vibrating saw, but the cut, as your next question implies, will be ragged unless you clamp a guide on the door.
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Richard RaustadSep 7 '13 at 3:24

Ideally, you should take the door off and use a power planer to remove small amounts from the bottom. The one at harbor freight is dirt cheap and could do a small job like this.
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Evil ElfSep 7 '13 at 15:23

3 Answers
3

Shave the bottom of the pocket door so it clears the tile. You have about an inch and a half of plug inside the hollow core door to trim. Don't shave more than 3/4" off the bottom. If you can, trim equal amounts off the top and bottom.